PLEASE NOTE TIME CHANGE FOR THE HAT FORUM FOR SATURDAY AUGUST 13th FOR THIS WEEK ONLY

to 10 a.m. - Noon

(Maintenance work at The 519)

Introductory QuestionDescribe a belief that you used to have, but changed your mind about.

Open-MindednessWhat do you think is a good way to think about open-mindedness?CertaintyCan we ever know anything with 100% certainty?Tree in the ForestA much-repeated question: "If a tree falls in a forest and no one is around to hear it, does it make a sound?"Occam's RazorAll else held equal, an explanation which makes fewer assumptions is more likely to be true than ones that rely on many assumptions. But suppose someone was to say "The woman down the road is a witch; she did it". This explanation feels simple, but what is wrong with it?Guess the RuleI will give a sequence of 3 numbers, which obeys a rule that I have in mind. The goal is to guess what the rule is by giving me sequences of 3 numbers of your own chosing, and I will say whether or not they follow my rule. The sequence is: 2, 4, 8.

Let others take some guesses if you are familiar with the puzzle.Terrorist-Camera Puzzle-Suppose that we have a city of 1,000,000 people. Assume that 10 of these people are terrorists, and the other 999,990 people are innocent citizens.-The mayor sets up some special cameras which are able to detect terrorists. Unfortunately, the accuracy rate isn't perfect.-When a terrorist walks in front of the camera, there is a 90% chance that the camera will correctly flag that person as a terrorist, and a 10% chance of marking them as innocent.-When an innocent citizen walks in front of a camera, it has a 99% chance of correctly marking them as innocent, and a 1% chance of mistakenly flagging them as a terrorist.

Suppose that someone walks in front of a camera, and it flags them as a terrorist. What is the probability that they are actually a terrorist? The answer may surprise you.